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if your game is going to use block graphics, then bounding boxes will work very well.

1. Only one object is moving at a time really, so two enemys can run into each other, one can run into another one - and then that other one can run into him right after, but you don't move everything at once and then try and figure out what collided after everything is moved, at least I wouldnt. you move something, and then check if the item you moved has collided with another object, and if it has - you undo the move (or figure out how far it is allowed to move without intersecting the other object)

2. that is entirely up to you, for all we mind you can just make it so we cant die, and thus wont have to worry about that

3. you will want to use boxes in this case because i think your building a block world and they should work very nicely for that, if by "like minecraft" you mean like its gameplay but your using all spheres or something else odd, then the method you could use to best and optimally detect collisions will be different.